This paper is concerned with the stability of a discrete kinetic approximation with a boundary scheme introduced by the authors in a previous work. We prove the weighted $L^2$-stability of the approximation by using an identity on three-point difference schemes for convection equations. With the weighted $L^2$-stability, the convergence of the discrete kinetic approximation can be directly established. Moreover, the present stability analysis, particularly the identity on three-point difference schemes, may be adapted to other kinetic methods. Numerical experiments are conducted to verify our stability results.

中文翻译：

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加权的 ${\mathrm{大号}}^2$界上不可压缩的Navier–Stokes方程的离散动力学逼近的稳定性

本文关注的是作者在先前的工作中引入的具有边界方案的离散动力学逼近的稳定性。我们证明了加权${\mathrm{大号}}^2$对流方程通过使用三点差分格式的恒等式求近似的稳定性。用加权${\mathrm{大号}}^2$-稳定性，可以直接建立离散动力学逼近的收敛。而且，当前的稳定性分析，特别是三点差分方案的同一性，可以适用于其他动力学方法。进行数值实验以验证我们的稳定性结果。